Figure Q2 shows a block diagram with a plant Gp(s) which is subjected to a disturbance R(s) and the reference input R(s). The response C(s) of the plant is governed by a controller G.(s). For the situation where there is no reference input (i.e. R(s) = 0), derive the closed loop transfer function relating the response C(s) to the disturbance D(s). Similarly derive the transfer function relating the response to the reference input R(s) and hence the response of the system to both inputs. (a) (b) The plant may be described by the transfer function 1 Gp(s) = · s(s + 7) It is proposed to apply a proportional plus derivative controller to the system such that G.(s) = Kp + Kas For the case where D(s) = 0, calculate the values of the gains K, and Ka if the performance requirements of the system are that it should have maximum overshoot of 15% and a natural frequency of 9 rad/s. Integral action with gain K; is added to the controller to form a PID controller. Find the values of K; for which the system remains stable. (c)

Figure Q2 shows a block diagram with a plant Gp(s) which is subjected to a disturbance R(s) and the reference input R(s). The response C(s) of the plant is governed by a controller G.(s). For the situation where there is no reference input (i.e. R(s) = 0), derive the closed loop transfer function relating the response C(s) to the disturbance D(s). Similarly derive the transfer function relating the response to the reference input R(s) and hence the response of the system to both inputs. (a) (b) The plant may be described by the transfer function 1 Gp(s) = · s(s + 7) It is proposed to apply a proportional plus derivative controller to the system such that G.(s) = Kp + Kas For the case where D(s) = 0, calculate the values of the gains K, and Ka if the performance requirements of the system are that it should have maximum overshoot of 15% and a natural frequency of 9 rad/s. Integral action with gain K; is added to the controller to form a PID controller. Find the values of K; for which the system remains stable. (c)

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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